ss4S2H {samplesize4surveys} | R Documentation |
The required sample size for testing a null hyphotesis for a single variance
Description
This function returns the minimum sample size required for testing a null hyphotesis regarding a single variance
Usage
ss4S2H(N, S2, S20, K = 0, DEFF = 1, conf = 0.95, power = 0.8, plot = FALSE)
Arguments
N |
The population size. |
S2 |
The value of the estimated variance |
S20 |
The value to test for the single variance |
K |
The excess kurtosis of the variable in the population. |
DEFF |
The design effect of the sample design. By default |
conf |
The statistical confidence. By default |
power |
The statistical power. By default |
plot |
Optionally plot the effect against the sample size. |
Details
We assume that it is of interest to test the following set of hyphotesis:
H_0: P - P_0 = 0 \ \ \ \ vs. \ \ \ \ H_a: P - P_0 = D > 0
Note that the minimun sample size, restricted to the predefined power \beta
and confidence 1-\alpha
, is defined by:
n = \frac{S2^2}{\frac{D^2}{(z_{1-\alpha} + z_{\beta})^2}\frac{(N-1)^3}{N^2(N*K+2N+2)}+\frac{S2^2}{N}}
Author(s)
Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>
References
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas
See Also
Examples
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 0)
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 2, DEFF = 2, power = 0.9)
ss4S2H(N = 10000, S2 = 120, S20 = 110, K = 2, DEFF = 2, power = 0.8, plot = TRUE)
#############################
# Example with BigLucy data #
#############################
data(BigLucy)
attach(BigLucy)
N <- nrow(BigLucy)
S2 <- var(BigLucy$Income)
# The minimum sample size for testing
# H_0: S2 - S2_0 = 0 vs. H_a: S2 - S2_0 = D = 8000
D = 8000
S20 = S2 - D
K <- kurtosis(BigLucy$Income)
ss4S2H(N, S2, S20, K, DEFF=1, conf = 0.99, power = 0.8, plot=TRUE)